Method of heat transfer



Feb. 26, 1935. o. e. WENDEL METHOD OF HEAT TRANSFER Original Filed Feb.12, l9 34 4 Sheets-Sheet 1 Feb. 26, 1935.

O. G. WENDEL METHOD OF HEAT TRANSFER 7 Original Filed Feb. 12, l934 4Sheets-Sheet 2 M/VEA TOIP 0770 6. WE/VDEZ M FM t yw Feb. 26, 1935. Q GwENDEL 1,992,561

METHOD OF HEAT TRANSFER Original Filed Feb. 12, 1934 4 Sheets-Sheet 3IAN/[N705 5y arm a. WEI/05L.

Feb. 26, 1935. o. G. WENDEL 1,992,561

METHOD OF HEAT TRANSFER Original Filed Feb. 12, 1934 4 Sheets-Sheet 4Patented Feb. 26, 1935 UNITED STATES METHOD OF HEAT TRANSFER m G.Wendel, Buffalo, N. Y., assignor to The American Radiator & StandardSanitary Mfg. Company, New York, N. Y., a corporation of DelawareOriginal application February 12, 1934, Serial No. 710,774. Divided andthis application June 6, 1934, SGI'iaINO. 729,267

3. Claims. (Cl. 2571) My invention relates to a method of heat transferespecially in connection with radiators.

The purpose of my invention is to provide a method and apparatustopractice heat transfer 5 from a fluid having a relatively high specificheat,

known as a prime fluid, through containing boundaries, such as castiron, to a fluid having a relatively low specific heat, denominated as asecondary fluid.

I have been successful in solving the problem of reducing the weight,the amount of space occupied and the friction, and of increasing therate of heat transfer by the radiator of my invention, which isparticularly useful in connection with heat transfer systems where airis blown over the radiators. My invention makes possible highefliciencies, as hereinafter pointed out, while, at the same time, notchanging the material, cast iron being employed.

Specifically, the foregoing advantageous results over the prior art havebeen secured by causing the fluid stream, such as air, to undulate to apoint approaching, but never attaining, detached flow, so that, at theupstream point of flow de- 25 flection, the pressure and velocity arematerially increased while the eddies are consequently reduced indiameter and acceleration, thus permitting more intimate contact at anincreased velocity with the more nearly virgin air near the 30 center ofthe stream and a continual removal of the fluid particles from thecenter of the stream to the boundary. There is a consequent reduction ofvelocity on the downstream cavity but, as this decreased velocity isimmediately followed by an increased velocity on the same boundarysurface by the next undulation, the diameters of the eddies areprevented from increasing to that size heretofore encountered innon-undulating flow as the time element between the alternating highvelocity-high pressure and low velocity-low pressure point isinsufficient to admit of reformation of an eddy diameter encountered innon-undulating flow.

In my invention, due to the alternate increased and decreasedvelocitiesand pressures, the heated boundary particles of the fluid arecontinually being replaced by cooler inner stream particles, thusproducing a greatly increased heating effect on the entire body of thefluid and producing maximum heat transfer from the prime to thesecondary fluid, requiring the minimum space, and requiring minimummaterial in the containing boundaries. 7

The energy expenditure necessary to produce such undulations isproportional to the angular change in direction added to thejncreasedfrictional resistance due to the velocity increase. The

loss due to angularity is sufficiently small as to be negligible. Agreatly increased rate of heat transfer is, therefore, produced byundetached undulatory flow at an expenditure of a negligible increase inenergy.

To secure the foregoing result in my method of heat transfer, I providea steam-containing body whose sides carry gently undulatory fins whichpreferably completely encircle the steam containing body. The bodyitself is longer in a plane at right angles to the direction of the finsthan in the direction of the fins and the steam or other heating orcooling fluid or gas is arranged at right angles to the direction of thefluid or gas passing over the outside of the body guided by on theinterior of the body of the radiator while the undulation of the finswithout change of direction of the air body moving on the outside of theradiator between the flns is suflicient to disturb the air film on theoutside of the body without back pressure and without detachment so thatthe undetached undulatory flow principle is practiced which I havediscovered is necessary for successful and economical heat transfer. Theair flow between the fins is of such a nature that it is continuous withan undetached contact with all surfaces of the metal boundariescomprising the wall of the radiator and the adjacent undulatory fins.

Another object of the invention is the practice of my method of heattransfer which is to so regulate the angularity of the undulations ofthe fins or ribs as to prevent the air stream leaving the surface of theradiator because theangular rate of undulation must be such as to avoiddetachment of the main air stream.

Another object is to provide that the general direction of the fins orribs shall be at an angle to they general direction of air flow; inother Words, one end of the rib will be higher than the other end of therib.

This application is a division of my application Ser. No. 710,774, filedFebruary 12, 1934.

In the accompamring drawings:

Figure 1 is a side elevation of one section of my radiator;

Figure 2 is an end elevation partially in section;

Figure 3 is a top plan view of the radiator section;

Figure 4 is a section on the line 44 of Figure 1;

Figure 5 is a section on the line 5-5 of Figure 1 showing the means ofattachment of two adjacent sections;

Figure 6 is an end view of one of the connecting nipples;

Figure '7 is a top plan view of two series of the sections showing thestaggered arrangement of one series with respect to the other andshowing in section the passageway through which air is forced over thesections;

Figure 8 is a diagrammatic view showing theprior art having parallelfins and the disadvantages thereof;

Figure 9 is a similar view showing the prior art with the conventionalsharp undulations and the disadvantages of detached undulatory flow;

Figure 10 is a detailed view of the present in vention showing theprinciples of undetached undulatory fiow which characterizes thisinvention.

Referring to the drawings in detail, 1 designates a radiator body,preferably of cast iron. This body is formed of thin side walls 2 andend walls 3. The side walls 2 are spaced in parallelism with one anotheradjacent to one another to form with the end walls a relatively narrowrectangular space for the confining of the prime fluid. The upper andlower portions of the body are enlarged at their respective oppositecorners forming large chambers 4 having areas in their side walls atsuch points of increased thickness as in the case of the collars 5 whichare internally machined at 6 to receive suitable connecting nipples orinlet or exit pipes or connecting nipples therefor.

It will be noted that the vertical dimension of the radiator body ismaterially greater than the horizontal dimension and that the horizontaldimension is materially greater than the width from side wall to sidewall. The line of fiow from inlet to outlet is over a smooth interiorsurface for the purposes hereinafter described.

On the exterior of the radiator body on opposite sides 2 on the exteriorthereof are a series of undulatory fins which are wedge-shaped insection and generally designated 7. In the construction shown there aretwo valleys and three hill portions on each fin marked respectively 8and 9. The fins completely encircle the body extending across the ends 3as at 10.

These end portions of the fins as at 10 are heavier than the side wallfins. Such end wall fins have the dual function of lending strength tothe very thin walls of the radiator body and form a continuous finsurface to facilitate the entry and exit of the secondary fluid, thatis, the air, into and from the space between the undulatory side fins,thus avoiding the vena contracta which oc-- curs when a sharp corneredwall is used, and thereby I minimize the losses due to changes invelocity and maintain continuous fluid contact with both the entry andparallel walls.

It will be noted that the undulations are very gentle in order to insurethe principle of undetached undulatory flow, as more fully explainedhereinafter. This is the vital principle goveming the construction andmethod of heat transfer of my invention.

In order to give a typical example of a successful radiator of thischaracter and without intending to limit myself in any manner, thefollowing are the dimensions of a successful radiator which I haveconstructed and operated. The distance from the entering edge to theexit edge of the end wall fins is 81% inches. The maximum depth of theend wall fins is A inch. The width of the side wall fins is inch, thethickness of the side wall is 1?; inch and the distance between theinterior of the side walls is inch. The inclination of the ribs in theinstance given amounts to a difference in elevation between the ends ofthe ribs of 1; of an inch.

The taper of the side wall fins is 3 degrees. The distance as indicatedon the drawings between thepoint of departure and the point of return ofeach undulation of the side wall fins is 11% inches. I have shown andsuccessfully used five of such undulations on-one side of the body in asingle fin. The distance between a line drawn from the crest of twoadjacent tops of undulations of the side wall fin to the bottom of theintermediate depression of the intermediate portion of the side wall finbetween such crests is approximately A, inch so that it can be seen thatthe undulation is very gentle and it is this discovery of such a gentleundulation which has made possible the extraordinary results from thisinvention. The radius of curvature and the dimensions thereof areindicated on Figure 1. I do not, of course, desire to be confined to anyof these dimensions, but I recite them in order to show a concretesuccessful example of the practice of my invention to enable others topractice it and successfully use it.

It will be noted that the fins are relatively thin, the dimensions beingas indicated. The end wall ribs which are continuations of the fins arewedge-shaped and thick relative to the side wall fins.

In practice, I can arrange, if desired, the sections either individuallyor in a. series in parallel or in two series with one series staggeredor in alignment with respect to the other series. This radiation may beused with convection currents but is preferably used with air deliveredunder pressure as by a fan and guided by a casing such as indicated at11a in the accompanying drawmgs.

When the sections are connected together in series they are so connectedby a hexagon nipple designated 12. When so connected the space betweenthe marginal edges adjacent the fins of the adjacent sections in theexample I have cited is 1% inches. The design, however, is not limitedto this dimension since by use of longer or shorter nipples thisdimension can be varied.

In actual test of this radiator of my invention in comparison with thebest radiator sections and the most efficient known in the art of castiron radiators today, I secure the following results:

When comparing the two radiators at equal friction, the radiator of myinvention weights 70% of the old radiator, requires 63% of the space ofthe old radiator, and provides 119% of the'heating surface of the oldradiator. I further find that the two stacks of the presentradiator,would do the work of 2.4 stacks of the old radiator.

When comparing the best radiator of the old art with my presentinvention on the basis of 'equal velocity of the air passing thereover,I find that my new radiator of this invention weighs 71% of the oldradiator, takes up 68% -of the space occupied by the old radiator andhas 128 of the heating surface of the old radiator. Two stacks of thenew radiator do the work of 2.3 stacks of the old radiator. The radiatorof this invention requires 83% of the friction of the old radiator.Furthermore, the new radiator stands a maximum hydraulic pressure of 200pounds gauge as compared with the maximum pressure of the old radiatorof pounds. The new radiator is, therefore, 30% lighter than the oldradiator and occupies 35% less space. It is superior whether compared onthe basis of equal friction or equal velocity. The significance'of thesecomparisons will be apparent when it is understood that one of theprimary uses of this radiation is in forced blast systems where thespace occupied, the weight involved, the resistance to air flow and therate of heat transfer are such vital factors as to constitute thedifference between failure and success in the operation of a forceddraft system. The radiator of my invention makes it possible to use castiron with all of its advantages in competition with radiators of othermaterials. While I do not desire to confine my invention to cast iron,yet its advantages become apparent when cast iron is used as a medium ofits embodiment and the basis of its comparison even with other materialsin other designs.

While not intending to limit my invention to all or a large part of thefollowing features, nevertheless the following is a summary of thenumerous features of operation and construction inherent in theconstruction and method of operation of the apparatus of my invention:

(1) An oblong, in section, steam body whose fiat sides carry undulatoryfins; while the sides of the steam-containing body are flat as shown inthe drawings, yet they could be made undulatory so long as theypreserved the hereinafter mentioned principle of undetached undulatoryflow.

(2) The width of the fins is constant and the edge of each fin isparallel to the fiat face of the radiator body. v

(3) The fins are undulatory out of a horizontal plane but are notundulatory out of a vertical plane and, therefore, there is no markedlateral change in direction of the air stream by reason of either thefins or of the body of the radiator.

(4) The fins completely encircle the entire radiator body both on thesides and on the ends thereby assisting in the entering of the air andthe exit of the air and at the same time improving the radiatorqualities of the structure.

(5) Such an arrangement provides a relief of the inlet between sectionsto reduce the vena contracta loss where the air enters. There is asimilar reduction of the loss at the exit in the same manner for thesame reason.

(6) The total width of the fins is so proportioned as to constitutesubstantially the total width of the body.

(7) The undulations of the fins are suflicient to bring about a wipingaction of the air on the fiat surface of the body to reduce the air filmon the surface of the body to increase heat transfer but such undulatoryarrangement is not sufil cient to set up turbulence or resistance to airflow so that the air movement will be sufficiently rapid to carry awaythe heat for maximum efiiciency. The foregoing statement must be read inthe light of the understanding of the principle of undetached undulatoryflow hereinafter explained. The fluid stream undulates to a pointapproaching never attaining detached fiow.

(8) The undulations of therib or fin in this section in this instancehave a depth only of onethirteenth of the distance between the crowns ofthe undulations. The undulations must be of such a character as topreserve the principle of this invention of undetached undulatory flow,which is a new feature of the invention and from which results theefliciency secured.

(9) The end ribs are heavy, wedge-shaped terminal ribs for reinforcingpurposes.

(10) The wallthickness is substantially twice as thick as the ribthickness while the rib or fin surfaces are twice as great as the bodysurface between the ribs so that the thinner ribs for heat transmissionpresent twice as great a heat radiating surface.

(11) The ribs are progressively thinner the further they are from theheat source so that there will be uniform distribution of heatthroughout the rib.

(12) The ribs are spaced on adjacent bodies from one another by adistance approximately the same as the combined width of adjacent ribsin order to provide a sufficient body of moving air to permit a velocitywhile securing maximum heat transfer. It is not intended, however, tolimit the probable application to this ratio.

(13) The straight side walls of the body give a free sweep for thetransverse steam flow to reduce the internal film on the interior of thebody of the radiator, thus increasing the efflciency of the heattransfer.

(14) The undulation of the fins without change of direction of the airbody moving between them is sufiicient to disturb the air film on theoutside of the body without back pressure and without detachment so thatthe undetached undulatory flow is secured.

(15) The air flow between the fins is ofsuch a nature that itiscontinuous with an undetached contact with all surfaces of the metalboundary. The surface must not be deprived of the close and intimatecontact with the fluid in order to prevent the loss in efliciency in thetransfer of convection heat. The formation and subsequent detachment oflarge eddies of air due to turbulence without intimate contact resultsin the expenditure of energy without adequate heat transfer. The presentinvention has the minimum area of boundary wall with the greatesttransfer of heat with the least energy expenditure. This is due to thefact that the fluid stream is caused by the fins to undulate to a pointapproaching but never attaining detached flow. The eddies arecorrespondingly reduced in size and the speed thereof accelerated. Thissecures intimate contact at increased velocities with the continualchange of the fluid particles from the center of the air stream totheboundary. Due to the alternate increased and decreased velocity inpressures, the air particles that are heated are continually supplantedby the cooler inner stream particles. So long as the angularity issufficiently minor, the energy expenditure necessary to produce theundulations, which energy expenditure is proportional to the angularchange in direction added to the increased frictional resistance due tothe velocity increase will be sufliciently small as of heat transferproduced by the undetached undulatory flow secured by this construction.

And, furthermore, the foregoing indicates that my invention and itsphysical features take into account these important propositions:

(1) The elimination of back pressure and the increase of velocity byusing a gentle undulatory flow of the air through channels of metalhaving substantially equal area on three sides and substantially equalheat distribution throughout the surface of the metal. a

(2) The movement of the air through such channels as to break up any airfilm on the surface of the metal without setting up undue turbulence andback pressure.

(3) The use of straight walls (or undulatory walls without detachment)of a main body so that the maximum velocity of the gas, water or steamwipes the film away on the interior of the wall decreasing its thicknessand increasing heat transfer; by having the straight body the film onthe interior and the exterior of the wall is reduced by the velocity ofthe steam and the velocity of the air.

(4) The essence of this invention is the discovcry of the principlereferred to herein as that of undetached undulatory flow. This meansthat the fluid stream undulates to a point approaching, but neverattaining, detached flow. Heat transfer is in proportion to thereduction in size of the eddies in diameter and the acceleration ofthose eddies to secure a more intimate contact and an increased velocitywith the cooler air near the center of the stream and a continuoussubstitution of the fluid partioles'from the center of the stream to theboundary.

As a basis for a full understanding of the principles of my method ofheat transfer and a typical construction by which my method may bepracticed, the following premises should be understood as the basis forthe practice of my invention.

As my purpose is to effect a heat transfer from the fluid having arelatively high specific heat; such as a prime fluid comprising steamthrough containing boundaries, such as cast iron, to a fluid having arelatively low specific heat, such as the secondary fluid air, it willbe understood that the prime fluid requires more contact area than thesecondary fluid. Therefore, I project from the boundaries of theradiator body on the outside where the air is flowing gently undulatorysurfaces of such undulation as to effect the practice of this invention.If the fins are made zigzag, in which various parts of the fins are atan abrupt angle to one another, then the object of the invention iscompletely destroyed. If the fins are made straight, again the object isdestroyed.

The side walls may be either flat or undulatory, the latter preferred,but, in any event, with an uninterrupted surface which permitscondensation to flow across the surfaces uniformly thus wetting andwiping the surface on the interior of the body with consequent increasein the rate of surface contact and the rate of heat transfer due to thecondensation on the walls having a higher specific heat than thecontainer gaseous fluid in the case of steam.

The secondary fluid, such as: air, on the outside of the body isconfined by the prime surface and the two projecting adjacent undulatoryfins are integrally connected to the prime surface and conduct heattherefrom. Those fins are so designed as to provide a comparatively evenflow of heat to the boundaries of the secondary fluid, and

the spacing is such that the maximum heat, both of convection andradiation, is imparted with the minimum surface friction resistance tofluid flow. The parallel fins are given a slight undulatory effect indirection of the fluid flow and are carried completely around the endsof the radiator body.

The relation of the angularity at any point of these undulations must besuch as to conform to the principles of turbulent flow that I observeand such undulations must be such that, at all points on them, therewill be uninterrupted surface contact between the air and the cast ironsurface.

The importance of this arrangement can best be understood by contrastwith the prior art. In the case of parallel fins, without undulations,that is, straight (Fig. 8) the fluid flow will have a velocity higherthan the average at a point midway between the fins with a gradualdecrease as the fin is approached. The friction of the fin surface onthe fiuid will cause minute swirls or eddies to form. These eddiesrevolving on independent axes will be detached and progressed downstream with the fluid flow but at much lower velocity than the true'stream, thus retarding the heat transfer which is governed by a functionof velocity at the point of contact of approximately the one-half power.These eddies further retard heat transfer in that they act as aninsulating media between the surface and the fluid, and prevent thedisplacement of the film in contact with the surface by fluid in themain stream, the removal of this eddy film from surface contact and thereplacement of eddying fluid with less highly heated fluid from the mainstream; and the increase of velocity at or near the boundary is,therefore, of prime importance especially as the heat transfer is in thenature of a one-half power. It is apparent that the alternatingincreased and decreased velocities will materially affect the growth,size and velocity of the eddies interposed between the main fluid streamand the boundary surface.

Turning to the other customary construction in the art of fins having aseries of portions at sharp (Fig. 9) angles to one another or havingfins that are sharply undulatory giving marked changes in direction,then the angle of undulation will be increased materially and the airflow will be changed in direction a number of times during the passagebetween the fins. The fluid flow will be deflected sharply with anexpenditure of energy relative to the acuteness of angularity of the airpath. The main stream will become detached from the boundary forming alow pressure area on the down stream,acute angle region between thestream and the boundary and a swirl or large eddy will be formed havinga diameter approaching the maximum distance between the parallel of thefluid stream and the maximum depth of the boundary therefrom. Thesurface will be thus deprived of intimate contact with the fluid losingits value in the transfer of convected heat, thus materially reducingits effectiveness.

The formation and subsequent detachment of these larger eddies imposegreatly increased turbulence without intimate contact with a consequentincrease of energy expended in producing flow between these twoextremes, i. e., parallel straight flow and alternate detached surfacefiow, which has characterized the prior art; I have found that there isa principle of construction which, when practiced, will produce thegreatest transfer of heat for the least energy expenditure with theminimum area of boundary wall permitting a marked decrease in the weightof cast iron employed, a decrease in size, a reduction in resistance toairflow and without a decrease in velocity.

The principle I have embodied in my invention, in my construction andmethod of operation is to so arrange in undulations of the fins as tosecure a continuous undetached contact with -all surfaces of theboundary which I call undetached' undulatory flow (Figs. 1 to 8 and Fig.10).

To the foregoing as a feature of my invention, I have added means forentry and exit of the air so as to minimize the losses due to changes invelocity and to maintain fluid contact with both entry and parallelwalls. At the point of entry, the vena contracta, which occurs with asharpcomered wall, is largely avoided.

By the practice of the invention embodying my principles and methods, itis possible to use undulations vertically with respect to the streamline but also horizontal with respect to the main line of the stream.

Referring to Figure 8, it will be seen that it shows a diagramillustrating the use of parallel wall fins, the walls being designated13. The cone of entering air is designated 14 and two relatively thickstreams of turbulent eddies 15 serve to insulate the body 14 of air fromthe-hot walls 13 thereby cutting down heat transfer. This parallel flowtype is ineflicient for the reasons heretofore pointed out.-

Turning to the other form characteristic of the prior art, (Fig. 9)which either consists of sharp. undulations as shown, or angularundulations, it

will be noted that the cone of air has an even narrower or thinner coneof air designated 16. This cone of air only touches at intervals at 17the sharply bent walls 18 while the spaces therebetween in the deepvalleys 19 are filled with very large areas of turbulent air 20. Thisillustrates the detached undulatory flow characteristic of the otherclass of the prior art which is unsuccessful for heat'transfer.

Turning to Figure 10, which illustrates the present invention, it willbe noted that the body of air 21 passing between the fins 7 engages overa relatively. long area indicated at 22 the adjacent areas on thesurfaces of the fins '7 and whatever small eddies are set up as at 23are of very minor character but are sufficient to cause movement of thehot air which is quickly heated due to the diameter of the eddies 23being small andrdue to the fact that these eddies move easilyintoportions of the body of the cooler air 21 and exchange places with othersmall eddies of cold air, thereby effecting a rapid heat transfer. Itwill be further apparent upon studying these diagrams, which illustrategraphically the practical tests and laboratory research results that Ihave secured, that thebody of air passing through in Figure 10 is muchlarger than in Figures 8 and 9. Furthermore, the area of contact of thebody 21 of air in Figure 10 is much greater than in Figures 8 and 9. Itwill be observed that the deep areas of turbulence in Figures 8 and 9which actas insulation areas between the heated fins and the body ofcoldair 14 or 16 are absent ,in Figure 10 of the present invention.These factors are vital in a blast radiator where resistance to air flowmust be avoided, and where quantity of air delivered suitably heatedwith the least expenditure of horsepower to move the air is the primarycriterion of success.

By employing a construction which practices the principle of undetachedundulatory flow explained herein, the present construction avoids thedisadvantages and pitfalls of the prior art and 'makes possible the useof an economical, forced direction of flow of the heating medium 'in thegeneral direction of a straight line of flow and imparting to said fluidan undulatory motion, the troughs of said undulations extending belowthe crests to. an extent between approximately 11/64'and 13/64 of aninch from a straight line to which the crests of the undulations aretangent, and guiding the fluid passing over the heat exchange surface ina plurality of undulating parallel streams. I

2. In a method of heat transfer, passing a heating medium in onedirection on one side of a heat exchange surface; and passing a fluid tobe heated on the other side of said surface at an angle to the directionof flow of the heating medium in the general direction of a. straightline flow, and imparting to the fluid an undulatory motion as saidfluid. passes 7 over the heat exchange surface, and guiding the fluid asit passes over said surface in a plurality of undulating parallelstreams, the troughs of said undulations extending below the crests toan extent between approximately 11/64 and 13/64 of an inch from ahorizontal line to which the crests of the un-' dulations are tangent.

3. In a method of heat transfer, pasing a heating medium in onedirection on one side of a heat exchange surface; and passing a fluid tobe heated on the other side of said surface at an angle to the directionof flow of the heating medium in the general direction of a straightline flow, and imparting to'the fluid an undulatory motion as said fluidpasses over the heat exchange surface, guiding the fluid as it passesover said surface in a plin'ality of undulating parallel streams, thetroughs of said undulations extending below the crests to an extentbetween approximately 11/64 and 13/64 of an inch from a horizontal lineto which the crests 'of the undulations are. tangent, and guiding thestreams of fluid at the entry and exit of said streams with respect tothe heat exchange OTIO G. WENDE'L.

